# Chapter 1 (Functions and Limits) FSc Part 2 Math

Level: F.Sc (Pre-Engg)
Class: 2nd Year
Board: Punjab Textbook Board
Subject: Mathematics
Total Exercises: 5
Type: Notes

In this chapter we will read these topics:

• Define the terms function.
• Define independent and dependent variables.
• Who used the terms function.
• Who invented the symbolic way to write function.
• Define domain of a function.
• Define the co-domain of a function.
• Define the range of a function.
• Define the real-valued function.
• What is vertical line test of graph of a function.
• Define piece-wise function.
• Define Open interval.
• Define half closed interval.
• Define closed interval.
• Types of function.
• Define Polynomial function.
• Define Linear function.
• Define Identity function.
• Define Constant function.
• Define rational function.
• Define trigonometric function.
• Define the inverse trigonometric function.
• Define the exponential function.
• Composition of functions and Inverse of a function.
• Define the composition of functions.
• Define the inverse of a function.
• The Real-Valued function.
• Theorems on the limit of functions.
• Limits of important functions.
• Prove theorem when n is a negative integer.
• Prove theorem when n is a positive integer.
• Prove theorem when n is zero.
• State Sandwich Theorem.
• Define the limit of a function.
• Define Left Hand and Right-Hand Limit of a function.
• What is the criterion for the existence of a limit of a function?
• Continuous and Discontinuous functions.
• Define Continuous function.
• Discuss the continuity of function.
• Draw the graph.
• Graphs the curves of parametric equations.
• Find the graphical solution of the equations.

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